any turbo or supercharger will work with the engine. What you're looking for would be an exhaust manifold that would fit the Jspec 1.6, downpipe, an intercooler etc. or the proper belts for the supercharger. You could put a turbo of a lawnmower if you had the proper piping for it.
Come to think of it that would kick ass.
I've heard before that the BPT swap can go for aroun 3000$-3500$ with everything (ECU, motor, tranny, wiring harness etc). Personally, I'd rather go with the BPT because you would get more power than a turbo on a stock 1.6 Jspec. Plus the BPT is already built to handle a turbo, while a stock non-turbo mx3 motor is not. It may take some beefing of the internals which would cost $$$.